Honestly, I've been on both sides, reconstructionist and eclectic, and there's
always going to be someone offended by what you're doing, so I wouldn't worry too much about that.

I think you have to just go with what works for you. I think the ancient knowledge that has survived is very important in understanding the Gods, because we have to look at them through their own cultural lens at times, or know what would be considered pleasing or offensive, but that doesn't always mean you have to do everything in the exact same way... times change, after all. But there are some things, like understanding how the Greeks viewed purity and such, and how they purified places/people, or some of the main elements of ritual, which could be something easily brought into an eclectic path, to honor the culture the deity came from.
As far as holidays, personally what worked best for me was following the repeating monthly sacred days from the Greek calendar (which worked well, as there is one associated with each of the 'primary' deities I follow), and then the wheel of the year festivals, given a somewhat Greek twist, so I can honor the gods, but still feel connected to the cycles of nature around me (which do not match up as well with Greek cycles). I know people who worship Artemis who only follow her yearly sacred days. Some might not follow any of the Greek holidays. Again, it really comes down to what works for you.
Greek and Egyptian pantheons are two of the most understanding groups (although they hate each other lol!!!)
I wouldn't go that far... There are some cultural issues at play - where the Greeks imposed a lot of their symbolism onto Egyptian religion, but there was a lot of willing syncretism as well. There are people today who are Greco-Egyptian reconstructionists, and plenty of people (myself included) who worship both pantheons without issue.